Axel Peder Jensen was the son of a farmer, he was born in Kerteminde on the island of Funen. After training as a house painter (1900–1904), he attended the Technical School in Aalborg (1903–1907) before studying art at Kristian Zahrtmann's Kunstnernes Studieskoler in Copenhagen (1907–1908). From 1908 to 1910, he was a student with Johan Rohde. He travelled to Paris in 1911 with William Scharff and Olaf Rude.

As a pupil of Zahrtmann and a friend of Olaf Rude, Jais Nielsen and William Scharff, he was one of a small group of Danish modernists who exhibited with De Tretten and later at the Grønningen. Despite numerous portraits in his early years, he was primarily a landscape painter, deeply attached to the countryside where he spent most of his life. He had an acute sense of the changing seasons, the wind and the weather. He spent most of his time in Blokhus in Vendsyssel in the north of Jutland, painting fields, marshes and sand dunes, sometimes with a few figures and perhaps houses, trees or telephone poles to enhance the composition. Like Fritz Syberg before him, he was one of the few Danes who not only painted summer scenes but also the ploughed fields of the autumn and the cold and wet of winter. Any sense of sadness was however usually dispelled by the bright, colorful texture of his works.